Question

Light passes through a diffraction grating with a slit spacing of 0.001 mm. A viewing screen is 100 cm behind the grating.

If the light is blue, with a wavelength of 450 , at about what distance from the center of the interference pattern will the first-order maximum appear?

Answer 1

Answer:

The distance from the center of the interference pattern will the first-order maximum appear is 50.38 cm.

Explanation:

Given that,

Slit space= 0.001 mm

Distance = 100 cm

Wavelength = 450 nm

We need to calculate the angle

Using formula for diffraction maxima

For first order,

$d\sin\theta=m\lambda$

$\theta=\sin^{-1}(\dfrac{\lambda}{d})$

Put the value into the formula

$\theta=\sin^{-1}(\dfrac{450\times10^{-9}}{0.001\times10^{-3}})$

$\theta=26.74^{\circ}$

We need to calculate the distance from the center of the interference pattern will the first-order maximum appear

Using formula of distance

$y=D\tan\theta$

Put the value into the formula

$y=100\tan26.74$

$y=50.38\ cm$

Hence, The distance from the center of the interference pattern will the first-order maximum appear is 50.38 cm.